Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.9 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.70 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.47467i | − | 1.61867i | −0.587348 | − | 0.809334i | \(-0.699828\pi\) | ||
0.587348 | − | 0.809334i | \(-0.300172\pi\) | |||||||
\(3\) | −8.82514 | − | 1.76549i | −0.980571 | − | 0.196165i | ||||
\(4\) | −25.9214 | −1.62009 | ||||||||
\(5\) | 26.7513i | 1.07005i | 0.844836 | + | 0.535025i | \(0.179698\pi\) | ||||
−0.844836 | + | 0.535025i | \(0.820302\pi\) | |||||||
\(6\) | −11.4310 | + | 57.1399i | −0.317527 | + | 1.58722i | ||||
\(7\) | −48.5383 | −0.990578 | −0.495289 | − | 0.868728i | \(-0.664938\pi\) | ||||
−0.495289 | + | 0.868728i | \(0.664938\pi\) | |||||||
\(8\) | 64.2378i | 1.00372i | ||||||||
\(9\) | 74.7661 | + | 31.1614i | 0.923038 | + | 0.384708i | ||||
\(10\) | 173.206 | 1.73206 | ||||||||
\(11\) | 66.3235i | 0.548128i | 0.961711 | + | 0.274064i | \(0.0883680\pi\) | ||||
−0.961711 | + | 0.274064i | \(0.911632\pi\) | |||||||
\(12\) | 228.760 | + | 45.7639i | 1.58861 | + | 0.317805i | ||||
\(13\) | −17.1474 | −0.101464 | −0.0507319 | − | 0.998712i | \(-0.516155\pi\) | ||||
−0.0507319 | + | 0.998712i | \(0.516155\pi\) | |||||||
\(14\) | 314.270i | 1.60342i | ||||||||
\(15\) | 47.2291 | − | 236.084i | 0.209907 | − | 1.04926i | ||||
\(16\) | 1.17649 | 0.00459568 | ||||||||
\(17\) | − | 329.024i | − | 1.13849i | −0.822168 | − | 0.569245i | \(-0.807235\pi\) | ||
0.822168 | − | 0.569245i | \(-0.192765\pi\) | |||||||
\(18\) | 201.760 | − | 484.086i | 0.622715 | − | 1.49409i | ||||
\(19\) | 308.577 | 0.854785 | 0.427393 | − | 0.904066i | \(-0.359432\pi\) | ||||
0.427393 | + | 0.904066i | \(0.359432\pi\) | |||||||
\(20\) | − | 693.430i | − | 1.73358i | ||||||
\(21\) | 428.357 | + | 85.6938i | 0.971332 | + | 0.194317i | ||||
\(22\) | 429.423 | 0.887237 | ||||||||
\(23\) | − | 68.4764i | − | 0.129445i | −0.997903 | − | 0.0647225i | \(-0.979384\pi\) | ||
0.997903 | − | 0.0647225i | \(-0.0206162\pi\) | |||||||
\(24\) | 113.411 | − | 566.908i | 0.196894 | − | 0.984214i | ||||
\(25\) | −90.6302 | −0.145008 | ||||||||
\(26\) | 111.024i | 0.164236i | ||||||||
\(27\) | −604.806 | − | 407.002i | −0.829638 | − | 0.558302i | ||||
\(28\) | 1258.18 | 1.60482 | ||||||||
\(29\) | 178.384i | 0.212110i | 0.994360 | + | 0.106055i | \(0.0338219\pi\) | ||||
−0.994360 | + | 0.106055i | \(0.966178\pi\) | |||||||
\(30\) | −1528.56 | − | 305.793i | −1.69840 | − | 0.339770i | ||||
\(31\) | 80.5949 | 0.0838656 | 0.0419328 | − | 0.999120i | \(-0.486648\pi\) | ||||
0.0419328 | + | 0.999120i | \(0.486648\pi\) | |||||||
\(32\) | 1020.19i | 0.996277i | ||||||||
\(33\) | 117.093 | − | 585.314i | 0.107524 | − | 0.537478i | ||||
\(34\) | −2130.32 | −1.84284 | ||||||||
\(35\) | − | 1298.46i | − | 1.05997i | ||||||
\(36\) | −1938.04 | − | 807.746i | −1.49540 | − | 0.623261i | ||||
\(37\) | 1120.58 | 0.818541 | 0.409270 | − | 0.912413i | \(-0.365783\pi\) | ||||
0.409270 | + | 0.912413i | \(0.365783\pi\) | |||||||
\(38\) | − | 1997.94i | − | 1.38361i | ||||||
\(39\) | 151.328 | + | 30.2735i | 0.0994924 | + | 0.0199037i | ||||
\(40\) | −1718.44 | −1.07403 | ||||||||
\(41\) | 426.250i | 0.253569i | 0.991930 | + | 0.126785i | \(0.0404657\pi\) | ||||
−0.991930 | + | 0.126785i | \(0.959534\pi\) | |||||||
\(42\) | 554.840 | − | 2773.47i | 0.314535 | − | 1.57226i | ||||
\(43\) | 1032.93 | 0.558640 | 0.279320 | − | 0.960198i | \(-0.409891\pi\) | ||||
0.279320 | + | 0.960198i | \(0.409891\pi\) | |||||||
\(44\) | − | 1719.20i | − | 0.888015i | ||||||
\(45\) | −833.606 | + | 2000.09i | −0.411657 | + | 0.987698i | ||||
\(46\) | −443.362 | −0.209528 | ||||||||
\(47\) | − | 574.063i | − | 0.259874i | −0.991522 | − | 0.129937i | \(-0.958522\pi\) | ||
0.991522 | − | 0.129937i | \(-0.0414776\pi\) | |||||||
\(48\) | −10.3827 | − | 2.07709i | −0.00450639 | − | 0.000901513i | ||||
\(49\) | −45.0329 | −0.0187559 | ||||||||
\(50\) | 586.801i | 0.234720i | ||||||||
\(51\) | −580.888 | + | 2903.68i | −0.223332 | + | 1.11637i | ||||
\(52\) | 444.484 | 0.164380 | ||||||||
\(53\) | 409.120i | 0.145646i | 0.997345 | + | 0.0728230i | \(0.0232008\pi\) | ||||
−0.997345 | + | 0.0728230i | \(0.976799\pi\) | |||||||
\(54\) | −2635.21 | + | 3915.92i | −0.903706 | + | 1.34291i | ||||
\(55\) | −1774.24 | −0.586525 | ||||||||
\(56\) | − | 3117.99i | − | 0.994258i | ||||||
\(57\) | −2723.24 | − | 544.790i | −0.838177 | − | 0.167679i | ||||
\(58\) | 1154.98 | 0.343335 | ||||||||
\(59\) | − | 453.188i | − | 0.130189i | ||||||
\(60\) | −1224.24 | + | 6119.62i | −0.340068 | + | 1.69989i | ||||
\(61\) | 4085.24 | 1.09789 | 0.548944 | − | 0.835859i | \(-0.315030\pi\) | ||||
0.548944 | + | 0.835859i | \(0.315030\pi\) | |||||||
\(62\) | − | 521.826i | − | 0.135751i | ||||||
\(63\) | −3629.02 | − | 1512.52i | −0.914341 | − | 0.381083i | ||||
\(64\) | 6624.21 | 1.61724 | ||||||||
\(65\) | − | 458.714i | − | 0.108571i | ||||||
\(66\) | −3789.72 | − | 758.141i | −0.869999 | − | 0.174045i | ||||
\(67\) | 8024.54 | 1.78760 | 0.893800 | − | 0.448466i | \(-0.148029\pi\) | ||||
0.893800 | + | 0.448466i | \(0.148029\pi\) | |||||||
\(68\) | 8528.76i | 1.84445i | ||||||||
\(69\) | −120.894 | + | 604.313i | −0.0253926 | + | 0.126930i | ||||
\(70\) | −8407.11 | −1.71574 | ||||||||
\(71\) | − | 9533.81i | − | 1.89125i | −0.325254 | − | 0.945627i | \(-0.605450\pi\) | ||
0.325254 | − | 0.945627i | \(-0.394550\pi\) | |||||||
\(72\) | −2001.74 | + | 4802.81i | −0.386138 | + | 0.926468i | ||||
\(73\) | 6393.64 | 1.19978 | 0.599891 | − | 0.800082i | \(-0.295211\pi\) | ||||
0.599891 | + | 0.800082i | \(0.295211\pi\) | |||||||
\(74\) | − | 7255.40i | − | 1.32495i | ||||||
\(75\) | 799.824 | + | 160.007i | 0.142191 | + | 0.0284456i | ||||
\(76\) | −7998.76 | −1.38483 | ||||||||
\(77\) | − | 3219.23i | − | 0.542963i | ||||||
\(78\) | 196.011 | − | 979.799i | 0.0322175 | − | 0.161045i | ||||
\(79\) | −2585.51 | −0.414278 | −0.207139 | − | 0.978312i | \(-0.566415\pi\) | ||||
−0.207139 | + | 0.978312i | \(0.566415\pi\) | |||||||
\(80\) | 31.4727i | 0.00491761i | ||||||||
\(81\) | 4618.94 | + | 4659.63i | 0.703999 | + | 0.710201i | ||||
\(82\) | 2759.83 | 0.410444 | ||||||||
\(83\) | − | 3769.55i | − | 0.547183i | −0.961846 | − | 0.273592i | \(-0.911788\pi\) | ||
0.961846 | − | 0.273592i | \(-0.0882117\pi\) | |||||||
\(84\) | −11103.6 | − | 2221.30i | −1.57364 | − | 0.314811i | ||||
\(85\) | 8801.80 | 1.21824 | ||||||||
\(86\) | − | 6687.86i | − | 0.904254i | ||||||
\(87\) | 314.936 | − | 1574.27i | 0.0416086 | − | 0.207989i | ||||
\(88\) | −4260.48 | −0.550165 | ||||||||
\(89\) | 5967.21i | 0.753340i | 0.926347 | + | 0.376670i | \(0.122931\pi\) | ||||
−0.926347 | + | 0.376670i | \(0.877069\pi\) | |||||||
\(90\) | 12949.9 | + | 5397.33i | 1.59875 | + | 0.666337i | ||||
\(91\) | 832.305 | 0.100508 | ||||||||
\(92\) | 1775.00i | 0.209712i | ||||||||
\(93\) | −711.261 | − | 142.289i | −0.0822362 | − | 0.0164515i | ||||
\(94\) | −3716.87 | −0.420651 | ||||||||
\(95\) | 8254.84i | 0.914663i | ||||||||
\(96\) | 1801.13 | − | 9003.30i | 0.195435 | − | 0.976920i | ||||
\(97\) | 15383.8 | 1.63501 | 0.817503 | − | 0.575925i | \(-0.195358\pi\) | ||||
0.817503 | + | 0.575925i | \(0.195358\pi\) | |||||||
\(98\) | 291.573i | 0.0303595i | ||||||||
\(99\) | −2066.73 | + | 4958.75i | −0.210869 | + | 0.505943i | ||||
\(100\) | 2349.26 | 0.234926 | ||||||||
\(101\) | 10477.0i | 1.02706i | 0.858072 | + | 0.513530i | \(0.171663\pi\) | ||||
−0.858072 | + | 0.513530i | \(0.828337\pi\) | |||||||
\(102\) | 18800.4 | + | 3761.06i | 1.80703 | + | 0.361501i | ||||
\(103\) | 2261.28 | 0.213148 | 0.106574 | − | 0.994305i | \(-0.466012\pi\) | ||||
0.106574 | + | 0.994305i | \(0.466012\pi\) | |||||||
\(104\) | − | 1101.51i | − | 0.101841i | ||||||
\(105\) | −2292.42 | + | 11459.1i | −0.207929 | + | 1.03937i | ||||
\(106\) | 2648.92 | 0.235753 | ||||||||
\(107\) | − | 21108.2i | − | 1.84368i | −0.387576 | − | 0.921838i | \(-0.626688\pi\) | ||
0.387576 | − | 0.921838i | \(-0.373312\pi\) | |||||||
\(108\) | 15677.4 | + | 10550.1i | 1.34409 | + | 0.904498i | ||||
\(109\) | 5238.41 | 0.440906 | 0.220453 | − | 0.975398i | \(-0.429246\pi\) | ||||
0.220453 | + | 0.975398i | \(0.429246\pi\) | |||||||
\(110\) | 11487.6i | 0.949389i | ||||||||
\(111\) | −9889.29 | − | 1978.38i | −0.802637 | − | 0.160569i | ||||
\(112\) | −57.1050 | −0.00455237 | ||||||||
\(113\) | 10631.5i | 0.832605i | 0.909226 | + | 0.416302i | \(0.136674\pi\) | ||||
−0.909226 | + | 0.416302i | \(0.863326\pi\) | |||||||
\(114\) | −3527.34 | + | 17632.1i | −0.271417 | + | 1.35673i | ||||
\(115\) | 1831.83 | 0.138513 | ||||||||
\(116\) | − | 4623.97i | − | 0.343636i | ||||||
\(117\) | −1282.04 | − | 534.336i | −0.0936549 | − | 0.0390339i | ||||
\(118\) | −2934.24 | −0.210733 | ||||||||
\(119\) | 15970.3i | 1.12776i | ||||||||
\(120\) | 15165.5 | + | 3033.89i | 1.05316 | + | 0.210687i | ||||
\(121\) | 10242.2 | 0.699556 | ||||||||
\(122\) | − | 26450.6i | − | 1.77712i | ||||||
\(123\) | 752.539 | − | 3761.71i | 0.0497415 | − | 0.248642i | ||||
\(124\) | −2089.13 | −0.135870 | ||||||||
\(125\) | 14295.1i | 0.914884i | ||||||||
\(126\) | −9793.07 | + | 23496.7i | −0.616848 | + | 1.48001i | ||||
\(127\) | −24055.7 | −1.49145 | −0.745727 | − | 0.666252i | \(-0.767898\pi\) | ||||
−0.745727 | + | 0.666252i | \(0.767898\pi\) | |||||||
\(128\) | − | 26566.6i | − | 1.62149i | ||||||
\(129\) | −9115.71 | − | 1823.62i | −0.547786 | − | 0.109586i | ||||
\(130\) | −2970.02 | −0.175741 | ||||||||
\(131\) | 19555.5i | 1.13953i | 0.821807 | + | 0.569767i | \(0.192966\pi\) | ||||
−0.821807 | + | 0.569767i | \(0.807034\pi\) | |||||||
\(132\) | −3035.22 | + | 15172.2i | −0.174198 | + | 0.870762i | ||||
\(133\) | −14977.8 | −0.846731 | ||||||||
\(134\) | − | 51956.3i | − | 2.89353i | ||||||
\(135\) | 10887.8 | − | 16179.3i | 0.597411 | − | 0.887755i | ||||
\(136\) | 21135.8 | 1.14272 | ||||||||
\(137\) | 10205.1i | 0.543720i | 0.962337 | + | 0.271860i | \(0.0876388\pi\) | ||||
−0.962337 | + | 0.271860i | \(0.912361\pi\) | |||||||
\(138\) | 3912.73 | + | 782.751i | 0.205457 | + | 0.0411022i | ||||
\(139\) | −20686.8 | −1.07069 | −0.535344 | − | 0.844634i | \(-0.679818\pi\) | ||||
−0.535344 | + | 0.844634i | \(0.679818\pi\) | |||||||
\(140\) | 33657.9i | 1.71724i | ||||||||
\(141\) | −1013.50 | + | 5066.18i | −0.0509784 | + | 0.254825i | ||||
\(142\) | −61728.3 | −3.06131 | ||||||||
\(143\) | − | 1137.27i | − | 0.0556151i | ||||||
\(144\) | 87.9618 | + | 36.6611i | 0.00424198 | + | 0.00176799i | ||||
\(145\) | −4772.01 | −0.226968 | ||||||||
\(146\) | − | 41396.7i | − | 1.94205i | ||||||
\(147\) | 397.421 | + | 79.5050i | 0.0183915 | + | 0.00367925i | ||||
\(148\) | −29047.1 | −1.32611 | ||||||||
\(149\) | 30863.4i | 1.39018i | 0.718923 | + | 0.695090i | \(0.244635\pi\) | ||||
−0.718923 | + | 0.695090i | \(0.755365\pi\) | |||||||
\(150\) | 1035.99 | − | 5178.60i | 0.0460440 | − | 0.230160i | ||||
\(151\) | 20970.3 | 0.919709 | 0.459854 | − | 0.887994i | \(-0.347902\pi\) | ||||
0.459854 | + | 0.887994i | \(0.347902\pi\) | |||||||
\(152\) | 19822.3i | 0.857961i | ||||||||
\(153\) | 10252.8 | − | 24599.8i | 0.437987 | − | 1.05087i | ||||
\(154\) | −20843.5 | −0.878878 | ||||||||
\(155\) | 2156.01i | 0.0897405i | ||||||||
\(156\) | −3922.63 | − | 784.732i | −0.161186 | − | 0.0322457i | ||||
\(157\) | 38969.6 | 1.58098 | 0.790490 | − | 0.612475i | \(-0.209826\pi\) | ||||
0.790490 | + | 0.612475i | \(0.209826\pi\) | |||||||
\(158\) | 16740.3i | 0.670578i | ||||||||
\(159\) | 722.297 | − | 3610.54i | 0.0285707 | − | 0.142816i | ||||
\(160\) | −27291.3 | −1.06607 | ||||||||
\(161\) | 3323.73i | 0.128225i | ||||||||
\(162\) | 30169.6 | − | 29906.1i | 1.14958 | − | 1.13954i | ||||
\(163\) | −29092.1 | −1.09496 | −0.547482 | − | 0.836818i | \(-0.684413\pi\) | ||||
−0.547482 | + | 0.836818i | \(0.684413\pi\) | |||||||
\(164\) | − | 11049.0i | − | 0.410804i | ||||||
\(165\) | 15657.9 | + | 3132.40i | 0.575129 | + | 0.115056i | ||||
\(166\) | −24406.6 | −0.885709 | ||||||||
\(167\) | 30094.7i | 1.07909i | 0.841957 | + | 0.539545i | \(0.181404\pi\) | ||||
−0.841957 | + | 0.539545i | \(0.818596\pi\) | |||||||
\(168\) | −5504.79 | + | 27516.7i | −0.195039 | + | 0.974941i | ||||
\(169\) | −28267.0 | −0.989705 | ||||||||
\(170\) | − | 56988.8i | − | 1.97193i | ||||||
\(171\) | 23071.1 | + | 9615.70i | 0.788999 | + | 0.328843i | ||||
\(172\) | −26774.9 | −0.905046 | ||||||||
\(173\) | − | 31591.9i | − | 1.05556i | −0.849381 | − | 0.527781i | \(-0.823024\pi\) | ||
0.849381 | − | 0.527781i | \(-0.176976\pi\) | |||||||
\(174\) | −10192.9 | − | 2039.10i | −0.336665 | − | 0.0673505i | ||||
\(175\) | 4399.04 | 0.143642 | ||||||||
\(176\) | 78.0291i | 0.00251902i | ||||||||
\(177\) | −800.098 | + | 3999.44i | −0.0255386 | + | 0.127659i | ||||
\(178\) | 38635.7 | 1.21941 | ||||||||
\(179\) | − | 7027.75i | − | 0.219336i | −0.993968 | − | 0.109668i | \(-0.965021\pi\) | ||
0.993968 | − | 0.109668i | \(-0.0349788\pi\) | |||||||
\(180\) | 21608.2 | − | 51845.1i | 0.666921 | − | 1.60016i | ||||
\(181\) | 50951.9 | 1.55526 | 0.777631 | − | 0.628721i | \(-0.216421\pi\) | ||||
0.777631 | + | 0.628721i | \(0.216421\pi\) | |||||||
\(182\) | − | 5388.90i | − | 0.162689i | ||||||
\(183\) | −36052.8 | − | 7212.44i | −1.07656 | − | 0.215368i | ||||
\(184\) | 4398.77 | 0.129926 | ||||||||
\(185\) | 29977.0i | 0.875880i | ||||||||
\(186\) | −921.277 | + | 4605.18i | −0.0266296 | + | 0.133113i | ||||
\(187\) | 21822.0 | 0.624038 | ||||||||
\(188\) | 14880.5i | 0.421019i | ||||||||
\(189\) | 29356.3 | + | 19755.2i | 0.821821 | + | 0.553041i | ||||
\(190\) | 53447.4 | 1.48054 | ||||||||
\(191\) | 36553.1i | 1.00198i | 0.865454 | + | 0.500988i | \(0.167030\pi\) | ||||
−0.865454 | + | 0.500988i | \(0.832970\pi\) | |||||||
\(192\) | −58459.5 | − | 11695.0i | −1.58582 | − | 0.317246i | ||||
\(193\) | −34412.9 | −0.923862 | −0.461931 | − | 0.886916i | \(-0.652843\pi\) | ||||
−0.461931 | + | 0.886916i | \(0.652843\pi\) | |||||||
\(194\) | − | 99604.9i | − | 2.64653i | ||||||
\(195\) | −809.855 | + | 4048.21i | −0.0212980 | + | 0.106462i | ||||
\(196\) | 1167.31 | 0.0303862 | ||||||||
\(197\) | − | 20824.8i | − | 0.536597i | −0.963336 | − | 0.268298i | \(-0.913539\pi\) | ||
0.963336 | − | 0.268298i | \(-0.0864613\pi\) | |||||||
\(198\) | 32106.3 | + | 13381.4i | 0.818954 | + | 0.341328i | ||||
\(199\) | −67155.1 | −1.69579 | −0.847897 | − | 0.530161i | \(-0.822131\pi\) | ||||
−0.847897 | + | 0.530161i | \(0.822131\pi\) | |||||||
\(200\) | − | 5821.88i | − | 0.145547i | ||||||
\(201\) | −70817.6 | − | 14167.2i | −1.75287 | − | 0.350665i | ||||
\(202\) | 67835.4 | 1.66247 | ||||||||
\(203\) | − | 8658.47i | − | 0.210111i | ||||||
\(204\) | 15057.4 | − | 75267.4i | 0.361818 | − | 1.80862i | ||||
\(205\) | −11402.7 | −0.271332 | ||||||||
\(206\) | − | 14641.1i | − | 0.345015i | ||||||
\(207\) | 2133.82 | − | 5119.71i | 0.0497985 | − | 0.119483i | ||||
\(208\) | −20.1738 | −0.000466295 | ||||||||
\(209\) | 20465.9i | 0.468532i | ||||||||
\(210\) | 74193.9 | + | 14842.7i | 1.68240 | + | 0.336568i | ||||
\(211\) | 63630.6 | 1.42923 | 0.714613 | − | 0.699520i | \(-0.246603\pi\) | ||||
0.714613 | + | 0.699520i | \(0.246603\pi\) | |||||||
\(212\) | − | 10605.0i | − | 0.235959i | ||||||
\(213\) | −16831.8 | + | 84137.2i | −0.370999 | + | 1.85451i | ||||
\(214\) | −136669. | −2.98430 | ||||||||
\(215\) | 27632.1i | 0.597773i | ||||||||
\(216\) | 26144.9 | − | 38851.4i | 0.560376 | − | 0.832721i | ||||
\(217\) | −3911.94 | −0.0830754 | ||||||||
\(218\) | − | 33917.0i | − | 0.713681i | ||||||
\(219\) | −56424.7 | − | 11287.9i | −1.17647 | − | 0.235356i | ||||
\(220\) | 45990.7 | 0.950221 | ||||||||
\(221\) | 5641.89i | 0.115516i | ||||||||
\(222\) | −12809.3 | + | 64029.9i | −0.259909 | + | 1.29920i | ||||
\(223\) | 60412.0 | 1.21482 | 0.607412 | − | 0.794387i | \(-0.292208\pi\) | ||||
0.607412 | + | 0.794387i | \(0.292208\pi\) | |||||||
\(224\) | − | 49518.2i | − | 0.986890i | ||||||
\(225\) | −6776.06 | − | 2824.16i | −0.133848 | − | 0.0557859i | ||||
\(226\) | 68835.7 | 1.34771 | ||||||||
\(227\) | − | 45524.1i | − | 0.883466i | −0.897147 | − | 0.441733i | \(-0.854364\pi\) | ||
0.897147 | − | 0.441733i | \(-0.145636\pi\) | |||||||
\(228\) | 70590.1 | + | 14121.7i | 1.35792 | + | 0.271655i | ||||
\(229\) | 19054.3 | 0.363348 | 0.181674 | − | 0.983359i | \(-0.441848\pi\) | ||||
0.181674 | + | 0.983359i | \(0.441848\pi\) | |||||||
\(230\) | − | 11860.5i | − | 0.224206i | ||||||
\(231\) | −5683.51 | + | 28410.1i | −0.106511 | + | 0.532414i | ||||
\(232\) | −11459.0 | −0.212898 | ||||||||
\(233\) | − | 84699.7i | − | 1.56016i | −0.625678 | − | 0.780081i | \(-0.715178\pi\) | ||
0.625678 | − | 0.780081i | \(-0.284822\pi\) | |||||||
\(234\) | −3459.65 | + | 8300.81i | −0.0631830 | + | 0.151596i | ||||
\(235\) | 15356.9 | 0.278079 | ||||||||
\(236\) | 11747.3i | 0.210917i | ||||||||
\(237\) | 22817.5 | + | 4564.68i | 0.406229 | + | 0.0812670i | ||||
\(238\) | 103402. | 1.82547 | ||||||||
\(239\) | − | 102141.i | − | 1.78815i | −0.447918 | − | 0.894075i | \(-0.647834\pi\) | ||
0.447918 | − | 0.894075i | \(-0.352166\pi\) | |||||||
\(240\) | 55.5647 | − | 277.751i | 0.000964664 | − | 0.00482206i | ||||
\(241\) | 8557.27 | 0.147333 | 0.0736667 | − | 0.997283i | \(-0.476530\pi\) | ||||
0.0736667 | + | 0.997283i | \(0.476530\pi\) | |||||||
\(242\) | − | 66314.9i | − | 1.13235i | ||||||
\(243\) | −32536.2 | − | 49276.5i | −0.551004 | − | 0.834502i | ||||
\(244\) | −105895. | −1.77867 | ||||||||
\(245\) | − | 1204.69i | − | 0.0200697i | ||||||
\(246\) | −24355.9 | − | 4872.44i | −0.402470 | − | 0.0805150i | ||||
\(247\) | −5291.29 | −0.0867297 | ||||||||
\(248\) | 5177.24i | 0.0841773i | ||||||||
\(249\) | −6655.09 | + | 33266.8i | −0.107338 | + | 0.536552i | ||||
\(250\) | 92555.9 | 1.48089 | ||||||||
\(251\) | 43678.6i | 0.693300i | 0.937995 | + | 0.346650i | \(0.112681\pi\) | ||||
−0.937995 | + | 0.346650i | \(0.887319\pi\) | |||||||
\(252\) | 94069.3 | + | 39206.6i | 1.48131 | + | 0.617388i | ||||
\(253\) | 4541.59 | 0.0709524 | ||||||||
\(254\) | 155753.i | 2.41417i | ||||||||
\(255\) | −77677.1 | − | 15539.5i | −1.19457 | − | 0.238977i | ||||
\(256\) | −66022.6 | −1.00742 | ||||||||
\(257\) | − | 49137.2i | − | 0.743951i | −0.928243 | − | 0.371976i | \(-0.878681\pi\) | ||
0.928243 | − | 0.371976i | \(-0.121319\pi\) | |||||||
\(258\) | −11807.3 | + | 59021.3i | −0.177383 | + | 0.886685i | ||||
\(259\) | −54391.2 | −0.810828 | ||||||||
\(260\) | 11890.5i | 0.175895i | ||||||||
\(261\) | −5558.70 | + | 13337.1i | −0.0816004 | + | 0.195785i | ||||
\(262\) | 126616. | 1.84453 | ||||||||
\(263\) | 102582.i | 1.48306i | 0.670919 | + | 0.741531i | \(0.265900\pi\) | ||||
−0.670919 | + | 0.741531i | \(0.734100\pi\) | |||||||
\(264\) | 37599.3 | + | 7521.82i | 0.539475 | + | 0.107923i | ||||
\(265\) | −10944.5 | −0.155849 | ||||||||
\(266\) | 96976.5i | 1.37058i | ||||||||
\(267\) | 10535.0 | − | 52661.4i | 0.147779 | − | 0.738703i | ||||
\(268\) | −208007. | −2.89607 | ||||||||
\(269\) | 19982.6i | 0.276151i | 0.990422 | + | 0.138076i | \(0.0440917\pi\) | ||||
−0.990422 | + | 0.138076i | \(0.955908\pi\) | |||||||
\(270\) | −104756. | − | 70495.1i | −1.43698 | − | 0.967011i | ||||
\(271\) | 926.550 | 0.0126162 | 0.00630812 | − | 0.999980i | \(-0.497992\pi\) | ||||
0.00630812 | + | 0.999980i | \(0.497992\pi\) | |||||||
\(272\) | − | 387.094i | − | 0.00523213i | ||||||
\(273\) | −7345.20 | − | 1469.42i | −0.0985550 | − | 0.0197161i | ||||
\(274\) | 66074.6 | 0.880103 | ||||||||
\(275\) | − | 6010.91i | − | 0.0794831i | ||||||
\(276\) | 3133.75 | − | 15664.6i | 0.0411383 | − | 0.205638i | ||||
\(277\) | −127962. | −1.66771 | −0.833857 | − | 0.551981i | \(-0.813872\pi\) | ||||
−0.833857 | + | 0.551981i | \(0.813872\pi\) | |||||||
\(278\) | 133940.i | 1.73309i | ||||||||
\(279\) | 6025.76 | + | 2511.45i | 0.0774112 | + | 0.0322638i | ||||
\(280\) | 83410.3 | 1.06391 | ||||||||
\(281\) | 77722.8i | 0.984319i | 0.870505 | + | 0.492160i | \(0.163792\pi\) | ||||
−0.870505 | + | 0.492160i | \(0.836208\pi\) | |||||||
\(282\) | 32801.9 | + | 6562.09i | 0.412478 | + | 0.0825171i | ||||
\(283\) | 14238.3 | 0.177781 | 0.0888907 | − | 0.996041i | \(-0.471668\pi\) | ||||
0.0888907 | + | 0.996041i | \(0.471668\pi\) | |||||||
\(284\) | 247130.i | 3.06400i | ||||||||
\(285\) | 14573.8 | − | 72850.1i | 0.179425 | − | 0.896892i | ||||
\(286\) | −7363.48 | −0.0900224 | ||||||||
\(287\) | − | 20689.4i | − | 0.251180i | ||||||
\(288\) | −31790.4 | + | 76275.4i | −0.383276 | + | 0.919602i | ||||
\(289\) | −24735.6 | −0.296161 | ||||||||
\(290\) | 30897.2i | 0.367386i | ||||||||
\(291\) | −135764. | − | 27159.9i | −1.60324 | − | 0.320732i | ||||
\(292\) | −165732. | −1.94375 | ||||||||
\(293\) | 94699.3i | 1.10309i | 0.834145 | + | 0.551546i | \(0.185962\pi\) | ||||
−0.834145 | + | 0.551546i | \(0.814038\pi\) | |||||||
\(294\) | 514.769 | − | 2573.17i | 0.00595549 | − | 0.0297697i | ||||
\(295\) | 12123.3 | 0.139309 | ||||||||
\(296\) | 71983.7i | 0.821582i | ||||||||
\(297\) | 26993.8 | − | 40112.8i | 0.306021 | − | 0.454748i | ||||
\(298\) | 199830. | 2.25024 | ||||||||
\(299\) | 1174.19i | 0.0131340i | ||||||||
\(300\) | −20732.5 | − | 4147.59i | −0.230362 | − | 0.0460844i | ||||
\(301\) | −50136.5 | −0.553377 | ||||||||
\(302\) | − | 135776.i | − | 1.48870i | ||||||
\(303\) | 18497.1 | − | 92461.3i | 0.201474 | − | 1.00711i | ||||
\(304\) | 363.039 | 0.00392832 | ||||||||
\(305\) | 109285.i | 1.17480i | ||||||||
\(306\) | −159276. | − | 66383.7i | −1.70101 | − | 0.708955i | ||||
\(307\) | 118694. | 1.25937 | 0.629685 | − | 0.776850i | \(-0.283184\pi\) | ||||
0.629685 | + | 0.776850i | \(0.283184\pi\) | |||||||
\(308\) | 83446.9i | 0.879648i | ||||||||
\(309\) | −19956.1 | − | 3992.27i | −0.209006 | − | 0.0418122i | ||||
\(310\) | 13959.5 | 0.145260 | ||||||||
\(311\) | − | 11227.5i | − | 0.116082i | −0.998314 | − | 0.0580409i | \(-0.981515\pi\) | ||
0.998314 | − | 0.0580409i | \(-0.0184854\pi\) | |||||||
\(312\) | −1944.70 | + | 9720.98i | −0.0199776 | + | 0.0998621i | ||||
\(313\) | 43090.7 | 0.439840 | 0.219920 | − | 0.975518i | \(-0.429420\pi\) | ||||
0.219920 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(314\) | − | 252315.i | − | 2.55908i | ||||||
\(315\) | 40461.8 | − | 97080.9i | 0.407778 | − | 0.978391i | ||||
\(316\) | 67020.0 | 0.671166 | ||||||||
\(317\) | − | 34372.0i | − | 0.342047i | −0.985267 | − | 0.171024i | \(-0.945293\pi\) | ||
0.985267 | − | 0.171024i | \(-0.0547075\pi\) | |||||||
\(318\) | −23377.1 | − | 4676.63i | −0.231172 | − | 0.0462465i | ||||
\(319\) | −11831.1 | −0.116263 | ||||||||
\(320\) | 177206.i | 1.73053i | ||||||||
\(321\) | −37266.4 | + | 186283.i | −0.361665 | + | 1.80785i | ||||
\(322\) | 21520.0 | 0.207554 | ||||||||
\(323\) | − | 101529.i | − | 0.973165i | ||||||
\(324\) | −119729. | − | 120784.i | −1.14054 | − | 1.15059i | ||||
\(325\) | 1554.07 | 0.0147131 | ||||||||
\(326\) | 188362.i | 1.77238i | ||||||||
\(327\) | −46229.7 | − | 9248.35i | −0.432340 | − | 0.0864906i | ||||
\(328\) | −27381.3 | −0.254511 | ||||||||
\(329\) | 27864.0i | 0.257426i | ||||||||
\(330\) | 20281.2 | − | 101380.i | 0.186237 | − | 0.930943i | ||||
\(331\) | −75885.6 | −0.692633 | −0.346317 | − | 0.938118i | \(-0.612568\pi\) | ||||
−0.346317 | + | 0.938118i | \(0.612568\pi\) | |||||||
\(332\) | 97711.9i | 0.886485i | ||||||||
\(333\) | 83781.6 | + | 34918.9i | 0.755544 | + | 0.314899i | ||||
\(334\) | 194854. | 1.74669 | ||||||||
\(335\) | 214666.i | 1.91282i | ||||||||
\(336\) | 503.959 | + | 100.818i | 0.00446392 | + | 0.000893018i | ||||
\(337\) | 142500. | 1.25474 | 0.627371 | − | 0.778721i | \(-0.284131\pi\) | ||||
0.627371 | + | 0.778721i | \(0.284131\pi\) | |||||||
\(338\) | 183019.i | 1.60200i | ||||||||
\(339\) | 18769.9 | − | 93824.7i | 0.163328 | − | 0.816428i | ||||
\(340\) | −228155. | −1.97366 | ||||||||
\(341\) | 5345.33i | 0.0459691i | ||||||||
\(342\) | 62258.5 | − | 149378.i | 0.532288 | − | 1.27713i | ||||
\(343\) | 118726. | 1.00916 | ||||||||
\(344\) | 66352.9i | 0.560716i | ||||||||
\(345\) | −16166.1 | − | 3234.07i | −0.135821 | − | 0.0271714i | ||||
\(346\) | −204547. | −1.70860 | ||||||||
\(347\) | − | 184710.i | − | 1.53402i | −0.641635 | − | 0.767010i | \(-0.721744\pi\) | ||
0.641635 | − | 0.767010i | \(-0.278256\pi\) | |||||||
\(348\) | −8163.57 | + | 40807.2i | −0.0674096 | + | 0.336960i | ||||
\(349\) | −68094.4 | −0.559062 | −0.279531 | − | 0.960137i | \(-0.590179\pi\) | ||||
−0.279531 | + | 0.960137i | \(0.590179\pi\) | |||||||
\(350\) | − | 28482.3i | − | 0.232509i | ||||||
\(351\) | 10370.8 | + | 6979.02i | 0.0841782 | + | 0.0566474i | ||||
\(352\) | −67662.4 | −0.546087 | ||||||||
\(353\) | 2116.15i | 0.0169823i | 0.999964 | + | 0.00849116i | \(0.00270285\pi\) | ||||
−0.999964 | + | 0.00849116i | \(0.997297\pi\) | |||||||
\(354\) | 25895.1 | + | 5180.37i | 0.206638 | + | 0.0413385i | ||||
\(355\) | 255041. | 2.02374 | ||||||||
\(356\) | − | 154678.i | − | 1.22048i | ||||||
\(357\) | 28195.3 | − | 140940.i | 0.221228 | − | 1.10585i | ||||
\(358\) | −45502.4 | −0.355033 | ||||||||
\(359\) | − | 102400.i | − | 0.794532i | −0.917704 | − | 0.397266i | \(-0.869959\pi\) | ||
0.917704 | − | 0.397266i | \(-0.130041\pi\) | |||||||
\(360\) | −128481. | − | 53549.0i | −0.991368 | − | 0.413187i | ||||
\(361\) | −35100.9 | −0.269342 | ||||||||
\(362\) | − | 329897.i | − | 2.51745i | ||||||
\(363\) | −90388.8 | − | 18082.5i | −0.685964 | − | 0.137229i | ||||
\(364\) | −21574.5 | −0.162831 | ||||||||
\(365\) | 171038.i | 1.28383i | ||||||||
\(366\) | −46698.2 | + | 233430.i | −0.348609 | + | 1.74259i | ||||
\(367\) | 204790. | 1.52047 | 0.760233 | − | 0.649650i | \(-0.225085\pi\) | ||||
0.760233 | + | 0.649650i | \(0.225085\pi\) | |||||||
\(368\) | − | 80.5619i | − | 0.000594887i | ||||||
\(369\) | −13282.5 | + | 31869.0i | −0.0975501 | + | 0.234054i | ||||
\(370\) | 194091. | 1.41776 | ||||||||
\(371\) | − | 19858.0i | − | 0.144274i | ||||||
\(372\) | 18436.9 | + | 3688.34i | 0.133230 | + | 0.0266529i | ||||
\(373\) | −37570.6 | −0.270042 | −0.135021 | − | 0.990843i | \(-0.543110\pi\) | ||||
−0.135021 | + | 0.990843i | \(0.543110\pi\) | |||||||
\(374\) | − | 141290.i | − | 1.01011i | ||||||
\(375\) | 25237.8 | − | 126156.i | 0.179469 | − | 0.897109i | ||||
\(376\) | 36876.5 | 0.260840 | ||||||||
\(377\) | − | 3058.82i | − | 0.0215215i | ||||||
\(378\) | 127908. | − | 190072.i | 0.895191 | − | 1.33026i | ||||
\(379\) | 127620. | 0.888465 | 0.444233 | − | 0.895911i | \(-0.353476\pi\) | ||||
0.444233 | + | 0.895911i | \(0.353476\pi\) | |||||||
\(380\) | − | 213977.i | − | 1.48183i | ||||||
\(381\) | 212295. | + | 42470.0i | 1.46248 | + | 0.292572i | ||||
\(382\) | 236669. | 1.62187 | ||||||||
\(383\) | − | 67921.4i | − | 0.463030i | −0.972831 | − | 0.231515i | \(-0.925632\pi\) | ||
0.972831 | − | 0.231515i | \(-0.0743682\pi\) | |||||||
\(384\) | −46903.0 | + | 234454.i | −0.318081 | + | 1.58999i | ||||
\(385\) | 86118.5 | 0.580998 | ||||||||
\(386\) | 222812.i | 1.49543i | ||||||||
\(387\) | 77227.8 | + | 32187.4i | 0.515646 | + | 0.214914i | ||||
\(388\) | −398769. | −2.64885 | ||||||||
\(389\) | 81552.6i | 0.538938i | 0.963009 | + | 0.269469i | \(0.0868481\pi\) | ||||
−0.963009 | + | 0.269469i | \(0.913152\pi\) | |||||||
\(390\) | 26210.9 | + | 5243.54i | 0.172327 | + | 0.0344743i | ||||
\(391\) | −22530.3 | −0.147372 | ||||||||
\(392\) | − | 2892.81i | − | 0.0188256i | ||||||
\(393\) | 34525.1 | − | 172580.i | 0.223537 | − | 1.11739i | ||||
\(394\) | −134834. | −0.868572 | ||||||||
\(395\) | − | 69165.6i | − | 0.443298i | ||||||
\(396\) | 53572.5 | − | 128538.i | 0.341627 | − | 0.819672i | ||||
\(397\) | −20135.3 | −0.127754 | −0.0638772 | − | 0.997958i | \(-0.520347\pi\) | ||||
−0.0638772 | + | 0.997958i | \(0.520347\pi\) | |||||||
\(398\) | 434808.i | 2.74493i | ||||||||
\(399\) | 132181. | + | 26443.2i | 0.830280 | + | 0.166099i | ||||
\(400\) | −106.626 | −0.000666411 | ||||||||
\(401\) | − | 188063.i | − | 1.16954i | −0.811199 | − | 0.584770i | \(-0.801185\pi\) | ||
0.811199 | − | 0.584770i | \(-0.198815\pi\) | |||||||
\(402\) | −91728.2 | + | 458521.i | −0.567611 | + | 2.83731i | ||||
\(403\) | −1381.99 | −0.00850932 | ||||||||
\(404\) | − | 271580.i | − | 1.66393i | ||||||
\(405\) | −124651. | + | 123562.i | −0.759951 | + | 0.753315i | ||||
\(406\) | −56060.8 | −0.340100 | ||||||||
\(407\) | 74320.9i | 0.448665i | ||||||||
\(408\) | −186526. | − | 37315.0i | −1.12052 | − | 0.224162i | ||||
\(409\) | 19089.1 | 0.114114 | 0.0570571 | − | 0.998371i | \(-0.481828\pi\) | ||||
0.0570571 | + | 0.998371i | \(0.481828\pi\) | |||||||
\(410\) | 73828.9i | 0.439196i | ||||||||
\(411\) | 18017.0 | − | 90061.3i | 0.106659 | − | 0.533156i | ||||
\(412\) | −58615.6 | −0.345318 | ||||||||
\(413\) | 21997.0i | 0.128962i | ||||||||
\(414\) | −33148.4 | − | 13815.8i | −0.193403 | − | 0.0806073i | ||||
\(415\) | 100840. | 0.585514 | ||||||||
\(416\) | − | 17493.5i | − | 0.101086i | ||||||
\(417\) | 182563. | + | 36522.2i | 1.04989 | + | 0.210032i | ||||
\(418\) | 132510. | 0.758397 | ||||||||
\(419\) | 152039.i | 0.866018i | 0.901390 | + | 0.433009i | \(0.142548\pi\) | ||||
−0.901390 | + | 0.433009i | \(0.857452\pi\) | |||||||
\(420\) | 59422.7 | − | 297036.i | 0.336863 | − | 1.68388i | ||||
\(421\) | 166921. | 0.941776 | 0.470888 | − | 0.882193i | \(-0.343934\pi\) | ||||
0.470888 | + | 0.882193i | \(0.343934\pi\) | |||||||
\(422\) | − | 411987.i | − | 2.31344i | ||||||
\(423\) | 17888.6 | − | 42920.4i | 0.0999758 | − | 0.239874i | ||||
\(424\) | −26281.0 | −0.146187 | ||||||||
\(425\) | 29819.5i | 0.165091i | ||||||||
\(426\) | 544761. | + | 108981.i | 3.00183 | + | 0.600524i | ||||
\(427\) | −198291. | −1.08754 | ||||||||
\(428\) | 547155.i | 2.98692i | ||||||||
\(429\) | −2007.84 | + | 10036.6i | −0.0109098 | + | 0.0545346i | ||||
\(430\) | 178909. | 0.967597 | ||||||||
\(431\) | − | 1348.54i | − | 0.00725954i | −0.999993 | − | 0.00362977i | \(-0.998845\pi\) | ||
0.999993 | − | 0.00362977i | \(-0.00115539\pi\) | |||||||
\(432\) | −711.550 | − | 478.835i | −0.00381275 | − | 0.00256577i | ||||
\(433\) | 293401. | 1.56490 | 0.782449 | − | 0.622715i | \(-0.213970\pi\) | ||||
0.782449 | + | 0.622715i | \(0.213970\pi\) | |||||||
\(434\) | 25328.5i | 0.134472i | ||||||||
\(435\) | 42113.6 | + | 8424.92i | 0.222558 | + | 0.0445233i | ||||
\(436\) | −135787. | −0.714307 | ||||||||
\(437\) | − | 21130.3i | − | 0.110648i | ||||||
\(438\) | −73085.5 | + | 365332.i | −0.380963 | + | 1.90432i | ||||
\(439\) | −258719. | −1.34245 | −0.671227 | − | 0.741252i | \(-0.734233\pi\) | ||||
−0.671227 | + | 0.741252i | \(0.734233\pi\) | |||||||
\(440\) | − | 113973.i | − | 0.588704i | ||||||
\(441\) | −3366.93 | − | 1403.29i | −0.0173124 | − | 0.00721554i | ||||
\(442\) | 36529.4 | 0.186981 | ||||||||
\(443\) | − | 89500.4i | − | 0.456056i | −0.973655 | − | 0.228028i | \(-0.926772\pi\) | ||
0.973655 | − | 0.228028i | \(-0.0732277\pi\) | |||||||
\(444\) | 256344. | + | 51282.3i | 1.30034 | + | 0.260136i | ||||
\(445\) | −159630. | −0.806112 | ||||||||
\(446\) | − | 391148.i | − | 1.96640i | ||||||
\(447\) | 54489.0 | − | 272374.i | 0.272705 | − | 1.36317i | ||||
\(448\) | −321528. | −1.60200 | ||||||||
\(449\) | − | 14364.7i | − | 0.0712532i | −0.999365 | − | 0.0356266i | \(-0.988657\pi\) | ||
0.999365 | − | 0.0356266i | \(-0.0113427\pi\) | |||||||
\(450\) | −18285.5 | + | 43872.8i | −0.0902988 | + | 0.216656i | ||||
\(451\) | −28270.4 | −0.138988 | ||||||||
\(452\) | − | 275584.i | − | 1.34889i | ||||||
\(453\) | −185066. | − | 37022.8i | −0.901839 | − | 0.180415i | ||||
\(454\) | −294754. | −1.43004 | ||||||||
\(455\) | 22265.2i | 0.107548i | ||||||||
\(456\) | 34996.1 | − | 174935.i | 0.168302 | − | 0.841292i | ||||
\(457\) | −223969. | −1.07240 | −0.536198 | − | 0.844092i | \(-0.680140\pi\) | ||||
−0.536198 | + | 0.844092i | \(0.680140\pi\) | |||||||
\(458\) | − | 123371.i | − | 0.588140i | ||||||
\(459\) | −133913. | + | 198996.i | −0.635621 | + | 0.944535i | ||||
\(460\) | −47483.6 | −0.224403 | ||||||||
\(461\) | − | 293479.i | − | 1.38094i | −0.723361 | − | 0.690470i | \(-0.757404\pi\) | ||
0.723361 | − | 0.690470i | \(-0.242596\pi\) | |||||||
\(462\) | 183946. | + | 36798.9i | 0.861802 | + | 0.172405i | ||||
\(463\) | −197511. | −0.921361 | −0.460680 | − | 0.887566i | \(-0.652395\pi\) | ||||
−0.460680 | + | 0.887566i | \(0.652395\pi\) | |||||||
\(464\) | 209.868i | 0.000974788i | ||||||||
\(465\) | 3806.42 | − | 19027.1i | 0.0176040 | − | 0.0879969i | ||||
\(466\) | −548403. | −2.52539 | ||||||||
\(467\) | − | 368870.i | − | 1.69137i | −0.533680 | − | 0.845686i | \(-0.679191\pi\) | ||
0.533680 | − | 0.845686i | \(-0.320809\pi\) | |||||||
\(468\) | 33232.3 | + | 13850.7i | 0.151729 | + | 0.0632384i | ||||
\(469\) | −389497. | −1.77076 | ||||||||
\(470\) | − | 99430.9i | − | 0.450117i | ||||||
\(471\) | −343912. | − | 68800.4i | −1.55026 | − | 0.310134i | ||||
\(472\) | 29111.8 | 0.130673 | ||||||||
\(473\) | 68507.3i | 0.306206i | ||||||||
\(474\) | 29554.8 | − | 147736.i | 0.131544 | − | 0.657549i | ||||
\(475\) | −27966.4 | −0.123951 | ||||||||
\(476\) | − | 413971.i | − | 1.82707i | ||||||
\(477\) | −12748.7 | + | 30588.3i | −0.0560312 | + | 0.134437i | ||||
\(478\) | −661329. | −2.89442 | ||||||||
\(479\) | − | 329730.i | − | 1.43710i | −0.695475 | − | 0.718550i | \(-0.744806\pi\) | ||
0.695475 | − | 0.718550i | \(-0.255194\pi\) | |||||||
\(480\) | 240850. | + | 48182.5i | 1.04535 | + | 0.209125i | ||||
\(481\) | −19215.0 | −0.0830522 | ||||||||
\(482\) | − | 55405.5i | − | 0.238484i | ||||||
\(483\) | 5868.00 | − | 29332.3i | 0.0251534 | − | 0.125734i | ||||
\(484\) | −265492. | −1.13334 | ||||||||
\(485\) | 411535.i | 1.74954i | ||||||||
\(486\) | −319049. | + | 210662.i | −1.35078 | + | 0.891893i | ||||
\(487\) | −87884.6 | −0.370557 | −0.185279 | − | 0.982686i | \(-0.559319\pi\) | ||||
−0.185279 | + | 0.982686i | \(0.559319\pi\) | |||||||
\(488\) | 262427.i | 1.10197i | ||||||||
\(489\) | 256742. | + | 51361.7i | 1.07369 | + | 0.214794i | ||||
\(490\) | −7799.95 | −0.0324862 | ||||||||
\(491\) | − | 18504.7i | − | 0.0767570i | −0.999263 | − | 0.0383785i | \(-0.987781\pi\) | ||
0.999263 | − | 0.0383785i | \(-0.0122193\pi\) | |||||||
\(492\) | −19506.9 | + | 97508.8i | −0.0805856 | + | 0.402822i | ||||
\(493\) | 58692.7 | 0.241485 | ||||||||
\(494\) | 34259.4i | 0.140387i | ||||||||
\(495\) | −132653. | − | 55287.6i | −0.541385 | − | 0.225641i | ||||
\(496\) | 94.8193 | 0.000385419 | ||||||||
\(497\) | 462755.i | 1.87343i | ||||||||
\(498\) | 215391. | + | 43089.6i | 0.868500 | + | 0.173745i | ||||
\(499\) | 171794. | 0.689934 | 0.344967 | − | 0.938615i | \(-0.387890\pi\) | ||||
0.344967 | + | 0.938615i | \(0.387890\pi\) | |||||||
\(500\) | − | 370548.i | − | 1.48219i | ||||||
\(501\) | 53131.9 | − | 265590.i | 0.211680 | − | 1.05812i | ||||
\(502\) | 282805. | 1.12222 | ||||||||
\(503\) | 256618.i | 1.01426i | 0.861868 | + | 0.507132i | \(0.169294\pi\) | ||||
−0.861868 | + | 0.507132i | \(0.830706\pi\) | |||||||
\(504\) | 97161.0 | − | 233120.i | 0.382499 | − | 0.917739i | ||||
\(505\) | −280274. | −1.09901 | ||||||||
\(506\) | − | 29405.3i | − | 0.114848i | ||||||
\(507\) | 249460. | + | 49905.0i | 0.970476 | + | 0.194146i | ||||
\(508\) | 623556. | 2.41629 | ||||||||
\(509\) | − | 482881.i | − | 1.86382i | −0.362688 | − | 0.931911i | \(-0.618141\pi\) | ||
0.362688 | − | 0.931911i | \(-0.381859\pi\) | |||||||
\(510\) | −100613. | + | 502934.i | −0.386825 | + | 1.93362i | ||||
\(511\) | −310336. | −1.18848 | ||||||||
\(512\) | 2409.45i | 0.00919132i | ||||||||
\(513\) | −186630. | − | 125592.i | −0.709162 | − | 0.477228i | ||||
\(514\) | −318148. | −1.20421 | ||||||||
\(515\) | 60492.2i | 0.228079i | ||||||||
\(516\) | 236292. | + | 47270.8i | 0.887462 | + | 0.177539i | ||||
\(517\) | 38073.8 | 0.142444 | ||||||||
\(518\) | 352165.i | 1.31246i | ||||||||
\(519\) | −55775.1 | + | 278803.i | −0.207065 | + | 1.03505i | ||||
\(520\) | 29466.8 | 0.108975 | ||||||||
\(521\) | − | 55186.5i | − | 0.203309i | −0.994820 | − | 0.101655i | \(-0.967586\pi\) | ||
0.994820 | − | 0.101655i | \(-0.0324137\pi\) | |||||||
\(522\) | 86353.4 | + | 35990.8i | 0.316912 | + | 0.132084i | ||||
\(523\) | −20140.8 | −0.0736330 | −0.0368165 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368165 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(524\) | − | 506907.i | − | 1.84614i | ||||||
\(525\) | −38822.1 | − | 7766.45i | −0.140851 | − | 0.0281776i | ||||
\(526\) | 664184. | 2.40059 | ||||||||
\(527\) | − | 26517.6i | − | 0.0954802i | ||||||
\(528\) | 137.760 | − | 688.618i | 0.000494144 | − | 0.00247008i | ||||
\(529\) | 275152. | 0.983244 | ||||||||
\(530\) | 70861.9i | 0.252267i | ||||||||
\(531\) | 14121.9 | − | 33883.1i | 0.0500847 | − | 0.120169i | ||||
\(532\) | 388246. | 1.37178 | ||||||||
\(533\) | − | 7309.06i | − | 0.0257281i | ||||||
\(534\) | −340965. | − | 68210.9i | −1.19572 | − | 0.239206i | ||||
\(535\) | 564672. | 1.97283 | ||||||||
\(536\) | 515479.i | 1.79424i | ||||||||
\(537\) | −12407.4 | + | 62020.9i | −0.0430262 | + | 0.215075i | ||||
\(538\) | 129381. | 0.446997 | ||||||||
\(539\) | − | 2986.74i | − | 0.0102806i | ||||||
\(540\) | −282228. | + | 419391.i | −0.967858 | + | 1.43824i | ||||
\(541\) | −169569. | −0.579366 | −0.289683 | − | 0.957123i | \(-0.593550\pi\) | ||||
−0.289683 | + | 0.957123i | \(0.593550\pi\) | |||||||
\(542\) | − | 5999.11i | − | 0.0204215i | ||||||
\(543\) | −449658. | − | 89955.0i | −1.52504 | − | 0.305088i | ||||
\(544\) | 335666. | 1.13425 | ||||||||
\(545\) | 140134.i | 0.471792i | ||||||||
\(546\) | −9514.05 | + | 47557.8i | −0.0319139 | + | 0.159528i | ||||
\(547\) | −395041. | −1.32029 | −0.660143 | − | 0.751140i | \(-0.729504\pi\) | ||||
−0.660143 | + | 0.751140i | \(0.729504\pi\) | |||||||
\(548\) | − | 264530.i | − | 0.880874i | ||||||
\(549\) | 305437. | + | 127302.i | 1.01339 | + | 0.422366i | ||||
\(550\) | −38918.7 | −0.128657 | ||||||||
\(551\) | 55045.4i | 0.181308i | ||||||||
\(552\) | −38819.8 | − | 7765.98i | −0.127402 | − | 0.0254870i | ||||
\(553\) | 125496. | 0.410374 | ||||||||
\(554\) | 828512.i | 2.69948i | ||||||||
\(555\) | 52924.0 | − | 264551.i | 0.171817 | − | 0.858862i | ||||
\(556\) | 536230. | 1.73461 | ||||||||
\(557\) | 322463.i | 1.03937i | 0.854358 | + | 0.519684i | \(0.173950\pi\) | ||||
−0.854358 | + | 0.519684i | \(0.826050\pi\) | |||||||
\(558\) | 16260.8 | − | 39014.9i | 0.0522244 | − | 0.125303i | ||||
\(559\) | −17712.0 | −0.0566818 | ||||||||
\(560\) | − | 1527.63i | − | 0.00487127i | ||||||
\(561\) | −192582. | − | 38526.5i | −0.611914 | − | 0.122415i | ||||
\(562\) | 503230. | 1.59329 | ||||||||
\(563\) | 434134.i | 1.36964i | 0.728711 | + | 0.684821i | \(0.240120\pi\) | ||||
−0.728711 | + | 0.684821i | \(0.759880\pi\) | |||||||
\(564\) | 26271.4 | − | 131323.i | 0.0825894 | − | 0.412839i | ||||
\(565\) | −284407. | −0.890929 | ||||||||
\(566\) | − | 92188.5i | − | 0.287769i | ||||||
\(567\) | −224195. | − | 226170.i | −0.697366 | − | 0.703509i | ||||
\(568\) | 612431. | 1.89828 | ||||||||
\(569\) | 32540.0i | 0.100506i | 0.998737 | + | 0.0502531i | \(0.0160028\pi\) | ||||
−0.998737 | + | 0.0502531i | \(0.983997\pi\) | |||||||
\(570\) | −471680. | − | 94360.8i | −1.45177 | − | 0.290430i | ||||
\(571\) | −42779.4 | −0.131209 | −0.0656043 | − | 0.997846i | \(-0.520898\pi\) | ||||
−0.0656043 | + | 0.997846i | \(0.520898\pi\) | |||||||
\(572\) | 29479.7i | 0.0901014i | ||||||||
\(573\) | 64534.1 | − | 322586.i | 0.196553 | − | 0.982509i | ||||
\(574\) | −133957. | −0.406577 | ||||||||
\(575\) | 6206.02i | 0.0187706i | ||||||||
\(576\) | 495266. | + | 206419.i | 1.49277 | + | 0.622165i | ||||
\(577\) | 625011. | 1.87731 | 0.938655 | − | 0.344858i | \(-0.112073\pi\) | ||||
0.938655 | + | 0.344858i | \(0.112073\pi\) | |||||||
\(578\) | 160155.i | 0.479386i | ||||||||
\(579\) | 303699. | + | 60755.6i | 0.905912 | + | 0.181230i | ||||
\(580\) | 123697. | 0.367708 | ||||||||
\(581\) | 182967.i | 0.542028i | ||||||||
\(582\) | −175851. | + | 879027.i | −0.519158 | + | 2.59511i | ||||
\(583\) | −27134.3 | −0.0798327 | ||||||||
\(584\) | 410713.i | 1.20424i | ||||||||
\(585\) | 14294.2 | − | 34296.3i | 0.0417683 | − | 0.100216i | ||||
\(586\) | 613147. | 1.78554 | ||||||||
\(587\) | 161202.i | 0.467838i | 0.972256 | + | 0.233919i | \(0.0751551\pi\) | ||||
−0.972256 | + | 0.233919i | \(0.924845\pi\) | |||||||
\(588\) | −10301.7 | − | 2060.88i | −0.0297958 | − | 0.00596071i | ||||
\(589\) | 24869.8 | 0.0716871 | ||||||||
\(590\) | − | 78494.7i | − | 0.225495i | ||||||
\(591\) | −36765.9 | + | 183782.i | −0.105262 | + | 0.526171i | ||||
\(592\) | 1318.36 | 0.00376175 | ||||||||
\(593\) | 57859.8i | 0.164539i | 0.996610 | + | 0.0822693i | \(0.0262168\pi\) | ||||
−0.996610 | + | 0.0822693i | \(0.973783\pi\) | |||||||
\(594\) | −259718. | − | 174776.i | −0.736086 | − | 0.495346i | ||||
\(595\) | −427225. | −1.20676 | ||||||||
\(596\) | − | 800022.i | − | 2.25221i | ||||||
\(597\) | 592653. | + | 118562.i | 1.66285 | + | 0.332656i | ||||
\(598\) | 7602.50 | 0.0212595 | ||||||||
\(599\) | 290228.i | 0.808882i | 0.914564 | + | 0.404441i | \(0.132534\pi\) | ||||
−0.914564 | + | 0.404441i | \(0.867466\pi\) | |||||||
\(600\) | −10278.5 | + | 51378.9i | −0.0285513 | + | 0.142719i | ||||
\(601\) | −385928. | −1.06846 | −0.534229 | − | 0.845340i | \(-0.679398\pi\) | ||||
−0.534229 | + | 0.845340i | \(0.679398\pi\) | |||||||
\(602\) | 324617.i | 0.895733i | ||||||||
\(603\) | 599963. | + | 250056.i | 1.65002 | + | 0.687704i | ||||
\(604\) | −543579. | −1.49001 | ||||||||
\(605\) | 273992.i | 0.748560i | ||||||||
\(606\) | −598657. | − | 119763.i | −1.63017 | − | 0.326119i | ||||
\(607\) | 508784. | 1.38088 | 0.690440 | − | 0.723389i | \(-0.257417\pi\) | ||||
0.690440 | + | 0.723389i | \(0.257417\pi\) | |||||||
\(608\) | 314807.i | 0.851603i | ||||||||
\(609\) | −15286.4 | + | 76412.2i | −0.0412166 | + | 0.206029i | ||||
\(610\) | 707587. | 1.90160 | ||||||||
\(611\) | 9843.67i | 0.0263678i | ||||||||
\(612\) | −265768. | + | 637662.i | −0.709577 | + | 1.70250i | ||||
\(613\) | −293162. | −0.780167 | −0.390083 | − | 0.920780i | \(-0.627554\pi\) | ||||
−0.390083 | + | 0.920780i | \(0.627554\pi\) | |||||||
\(614\) | − | 768508.i | − | 2.03850i | ||||||
\(615\) | 100631. | + | 20131.4i | 0.266060 | + | 0.0532259i | ||||
\(616\) | 206796. | 0.544981 | ||||||||
\(617\) | − | 124210.i | − | 0.326276i | −0.986603 | − | 0.163138i | \(-0.947838\pi\) | ||
0.986603 | − | 0.163138i | \(-0.0521615\pi\) | |||||||
\(618\) | −25848.6 | + | 129209.i | −0.0676801 | + | 0.338312i | ||||
\(619\) | 326503. | 0.852131 | 0.426065 | − | 0.904692i | \(-0.359899\pi\) | ||||
0.426065 | + | 0.904692i | \(0.359899\pi\) | |||||||
\(620\) | − | 55886.9i | − | 0.145387i | ||||||
\(621\) | −27870.0 | + | 41414.9i | −0.0722693 | + | 0.107392i | ||||
\(622\) | −72694.6 | −0.187898 | ||||||||
\(623\) | − | 289638.i | − | 0.746242i | ||||||
\(624\) | 178.036 | + | 35.6166i | 0.000457235 | + | 9.14709e-5i | ||||
\(625\) | −439055. | −1.12398 | ||||||||
\(626\) | − | 278998.i | − | 0.711955i | ||||||
\(627\) | 36132.4 | − | 180615.i | 0.0919097 | − | 0.459428i | ||||
\(628\) | −1.01015e6 | −2.56133 | ||||||||
\(629\) | − | 368698.i | − | 0.931901i | ||||||
\(630\) | −628567. | − | 261977.i | −1.58369 | − | 0.660058i | ||||
\(631\) | −421608. | −1.05889 | −0.529445 | − | 0.848345i | \(-0.677600\pi\) | ||||
−0.529445 | + | 0.848345i | \(0.677600\pi\) | |||||||
\(632\) | − | 166087.i | − | 0.415817i | ||||||
\(633\) | −561549. | − | 112339.i | −1.40146 | − | 0.280365i | ||||
\(634\) | −222547. | −0.553661 | ||||||||
\(635\) | − | 643519.i | − | 1.59593i | ||||||
\(636\) | −18722.9 | + | 93590.2i | −0.0462871 | + | 0.231375i | ||||
\(637\) | 772.195 | 0.00190304 | ||||||||
\(638\) | 76602.3i | 0.188192i | ||||||||
\(639\) | 297086. | − | 712806.i | 0.727581 | − | 1.74570i | ||||
\(640\) | 710689. | 1.73508 | ||||||||
\(641\) | − | 135933.i | − | 0.330834i | −0.986224 | − | 0.165417i | \(-0.947103\pi\) | ||
0.986224 | − | 0.165417i | \(-0.0528970\pi\) | |||||||
\(642\) | 1.20612e6 | + | 241288.i | 2.92632 | + | 0.585416i | ||||
\(643\) | −293832. | −0.710686 | −0.355343 | − | 0.934736i | \(-0.615636\pi\) | ||||
−0.355343 | + | 0.934736i | \(0.615636\pi\) | |||||||
\(644\) | − | 86155.6i | − | 0.207736i | ||||||
\(645\) | 48784.1 | − | 243857.i | 0.117262 | − | 0.586159i | ||||
\(646\) | −657369. | −1.57523 | ||||||||
\(647\) | 585214.i | 1.39800i | 0.715123 | + | 0.698999i | \(0.246371\pi\) | ||||
−0.715123 | + | 0.698999i | \(0.753629\pi\) | |||||||
\(648\) | −299324. | + | 296710.i | −0.712840 | + | 0.706615i | ||||
\(649\) | 30057.0 | 0.0713602 | ||||||||
\(650\) | − | 10062.1i | − | 0.0238156i | ||||||
\(651\) | 34523.4 | + | 6906.48i | 0.0814613 | + | 0.0162965i | ||||
\(652\) | 754107. | 1.77394 | ||||||||
\(653\) | − | 449055.i | − | 1.05311i | −0.850142 | − | 0.526554i | \(-0.823484\pi\) | ||
0.850142 | − | 0.526554i | \(-0.176516\pi\) | |||||||
\(654\) | −59880.0 | + | 299322.i | −0.140000 | + | 0.699815i | ||||
\(655\) | −523135. | −1.21936 | ||||||||
\(656\) | 501.480i | 0.00116532i | ||||||||
\(657\) | 478027. | + | 199235.i | 1.10744 | + | 0.461566i | ||||
\(658\) | 180410. | 0.416687 | ||||||||
\(659\) | − | 394456.i | − | 0.908297i | −0.890926 | − | 0.454149i | \(-0.849944\pi\) | ||
0.890926 | − | 0.454149i | \(-0.150056\pi\) | |||||||
\(660\) | −405874. | − | 81196.1i | −0.931759 | − | 0.186401i | ||||
\(661\) | 61363.2 | 0.140445 | 0.0702223 | − | 0.997531i | \(-0.477629\pi\) | ||||
0.0702223 | + | 0.997531i | \(0.477629\pi\) | |||||||
\(662\) | 491335.i | 1.12114i | ||||||||
\(663\) | 9960.70 | − | 49790.5i | 0.0226602 | − | 0.113271i | ||||
\(664\) | 242147. | 0.549217 | ||||||||
\(665\) | − | 400676.i | − | 0.906045i | ||||||
\(666\) | 226088. | − | 542458.i | 0.509718 | − | 1.22298i | ||||
\(667\) | 12215.1 | 0.0274565 | ||||||||
\(668\) | − | 780097.i | − | 1.74822i | ||||||
\(669\) | −533144. | − | 106657.i | −1.19122 | − | 0.238307i | ||||
\(670\) | 1.38990e6 | 3.09623 | ||||||||
\(671\) | 270947.i | 0.601783i | ||||||||
\(672\) | −87423.8 | + | 437005.i | −0.193594 | + | 0.967715i | ||||
\(673\) | 678204. | 1.49737 | 0.748687 | − | 0.662924i | \(-0.230685\pi\) | ||||
0.748687 | + | 0.662924i | \(0.230685\pi\) | |||||||
\(674\) | − | 922639.i | − | 2.03101i | ||||||
\(675\) | 54813.7 | + | 36886.7i | 0.120304 | + | 0.0809584i | ||||
\(676\) | 732719. | 1.60341 | ||||||||
\(677\) | 84970.9i | 0.185393i | 0.995694 | + | 0.0926964i | \(0.0295486\pi\) | ||||
−0.995694 | + | 0.0926964i | \(0.970451\pi\) | |||||||
\(678\) | −607484. | − | 121529.i | −1.32153 | − | 0.264374i | ||||
\(679\) | −746702. | −1.61960 | ||||||||
\(680\) | 565408.i | 1.22277i | ||||||||
\(681\) | −80372.3 | + | 401757.i | −0.173305 | + | 0.866301i | ||||
\(682\) | 34609.3 | 0.0744087 | ||||||||
\(683\) | 368714.i | 0.790403i | 0.918594 | + | 0.395201i | \(0.129325\pi\) | ||||
−0.918594 | + | 0.395201i | \(0.870675\pi\) | |||||||
\(684\) | −598036. | − | 249252.i | −1.27825 | − | 0.532754i | ||||
\(685\) | −272999. | −0.581808 | ||||||||
\(686\) | − | 768714.i | − | 1.63349i | ||||||
\(687\) | −168157. | − | 33640.2i | −0.356288 | − | 0.0712763i | ||||
\(688\) | 1215.23 | 0.00256733 | ||||||||
\(689\) | − | 7015.33i | − | 0.0147778i | ||||||
\(690\) | −20939.6 | + | 104670.i | −0.0439815 | + | 0.219850i | ||||
\(691\) | 431721. | 0.904164 | 0.452082 | − | 0.891976i | \(-0.350681\pi\) | ||||
0.452082 | + | 0.891976i | \(0.350681\pi\) | |||||||
\(692\) | 818906.i | 1.71010i | ||||||||
\(693\) | 100316. | − | 240689.i | 0.208882 | − | 0.501176i | ||||
\(694\) | −1.19594e6 | −2.48307 | ||||||||
\(695\) | − | 553397.i | − | 1.14569i | ||||||
\(696\) | 101127. | + | 20230.8i | 0.208761 | + | 0.0417632i | ||||
\(697\) | 140246. | 0.288686 | ||||||||
\(698\) | 440889.i | 0.904937i | ||||||||
\(699\) | −149536. | + | 747486.i | −0.306050 | + | 1.52985i | ||||
\(700\) | −114029. | −0.232713 | ||||||||
\(701\) | 165775.i | 0.337351i | 0.985672 | + | 0.168676i | \(0.0539490\pi\) | ||||
−0.985672 | + | 0.168676i | \(0.946051\pi\) | |||||||
\(702\) | 45186.9 | − | 67147.8i | 0.0916934 | − | 0.136257i | ||||
\(703\) | 345786. | 0.699676 | ||||||||
\(704\) | 439340.i | 0.886453i | ||||||||
\(705\) | −135527. | − | 27112.4i | −0.272676 | − | 0.0545495i | ||||
\(706\) | 13701.4 | 0.0274887 | ||||||||
\(707\) | − | 508538.i | − | 1.01738i | ||||||
\(708\) | 20739.7 | − | 103671.i | 0.0413747 | − | 0.206819i | ||||
\(709\) | −156571. | −0.311472 | −0.155736 | − | 0.987799i | \(-0.549775\pi\) | ||||
−0.155736 | + | 0.987799i | \(0.549775\pi\) | |||||||
\(710\) | − | 1.65131e6i | − | 3.27576i | ||||||
\(711\) | −193308. | − | 80567.9i | −0.382394 | − | 0.159376i | ||||
\(712\) | −383320. | −0.756139 | ||||||||
\(713\) | − | 5518.84i | − | 0.0108560i | ||||||
\(714\) | −912539. | − | 182555.i | −1.79001 | − | 0.358095i | ||||
\(715\) | 30423.5 | 0.0595110 | ||||||||
\(716\) | 182169.i | 0.355344i | ||||||||
\(717\) | −180329. | + | 901407.i | −0.350773 | + | 1.75341i | ||||
\(718\) | −663007. | −1.28608 | ||||||||
\(719\) | 731807.i | 1.41559i | 0.706416 | + | 0.707797i | \(0.250311\pi\) | ||||
−0.706416 | + | 0.707797i | \(0.749689\pi\) | |||||||
\(720\) | −980.731 | + | 2353.09i | −0.00189184 | + | 0.00453914i | ||||
\(721\) | −109759. | −0.211139 | ||||||||
\(722\) | 227267.i | 0.435976i | ||||||||
\(723\) | −75519.1 | − | 15107.8i | −0.144471 | − | 0.0289017i | ||||
\(724\) | −1.32074e6 | −2.51966 | ||||||||
\(725\) | − | 16167.0i | − | 0.0307577i | ||||||
\(726\) | −117078. | + | 585238.i | −0.222128 | + | 1.11035i | ||||
\(727\) | −131366. | −0.248549 | −0.124275 | − | 0.992248i | \(-0.539660\pi\) | ||||
−0.124275 | + | 0.992248i | \(0.539660\pi\) | |||||||
\(728\) | 53465.4i | 0.100881i | ||||||||
\(729\) | 200140. | + | 492315.i | 0.376598 | + | 0.926377i | ||||
\(730\) | 1.10741e6 | 2.07809 | ||||||||
\(731\) | − | 339857.i | − | 0.636007i | ||||||
\(732\) | 934539. | + | 186957.i | 1.74412 | + | 0.348914i | ||||
\(733\) | 145629. | 0.271044 | 0.135522 | − | 0.990774i | \(-0.456729\pi\) | ||||
0.135522 | + | 0.990774i | \(0.456729\pi\) | |||||||
\(734\) | − | 1.32595e6i | − | 2.46113i | ||||||
\(735\) | −2126.86 | + | 10631.5i | −0.00393699 | + | 0.0196798i | ||||
\(736\) | 69858.7 | 0.128963 | ||||||||
\(737\) | 532215.i | 0.979834i | ||||||||
\(738\) | 206342. | + | 86000.0i | 0.378856 | + | 0.157901i | ||||
\(739\) | 711310. | 1.30248 | 0.651238 | − | 0.758873i | \(-0.274250\pi\) | ||||
0.651238 | + | 0.758873i | \(0.274250\pi\) | |||||||
\(740\) | − | 777045.i | − | 1.41900i | ||||||
\(741\) | 46696.4 | + | 9341.72i | 0.0850446 | + | 0.0170134i | ||||
\(742\) | −128574. | −0.233531 | ||||||||
\(743\) | 356613.i | 0.645981i | 0.946402 | + | 0.322991i | \(0.104688\pi\) | ||||
−0.946402 | + | 0.322991i | \(0.895312\pi\) | |||||||
\(744\) | 9140.36 | − | 45689.8i | 0.0165127 | − | 0.0825418i | ||||
\(745\) | −825635. | −1.48756 | ||||||||
\(746\) | 243258.i | 0.437108i | ||||||||
\(747\) | 117464. | − | 281834.i | 0.210506 | − | 0.505071i | ||||
\(748\) | −565657. | −1.01100 | ||||||||
\(749\) | 1.02456e6i | 1.82630i | ||||||||
\(750\) | −816819. | − | 163406.i | −1.45212 | − | 0.290500i | ||||
\(751\) | −747008. | −1.32448 | −0.662240 | − | 0.749292i | \(-0.730394\pi\) | ||||
−0.662240 | + | 0.749292i | \(0.730394\pi\) | |||||||
\(752\) | − | 675.381i | − | 0.00119430i | ||||||
\(753\) | 77114.1 | − | 385470.i | 0.136002 | − | 0.679830i | ||||
\(754\) | −19804.9 | −0.0348361 | ||||||||
\(755\) | 560981.i | 0.984135i | ||||||||
\(756\) | −760955. | − | 512082.i | −1.33142 | − | 0.895975i | ||||
\(757\) | −376457. | −0.656937 | −0.328469 | − | 0.944515i | \(-0.606533\pi\) | ||||
−0.328469 | + | 0.944515i | \(0.606533\pi\) | |||||||
\(758\) | − | 826298.i | − | 1.43813i | ||||||
\(759\) | −40080.2 | − | 8018.13i | −0.0695738 | − | 0.0139184i | ||||
\(760\) | −530273. | −0.918062 | ||||||||
\(761\) | 1.05381e6i | 1.81968i | 0.414965 | + | 0.909838i | \(0.363794\pi\) | ||||
−0.414965 | + | 0.909838i | \(0.636206\pi\) | |||||||
\(762\) | 274979. | − | 1.37454e6i | 0.473577 | − | 2.36726i | ||||
\(763\) | −254263. | −0.436752 | ||||||||
\(764\) | − | 947508.i | − | 1.62329i | ||||||
\(765\) | 658076. | + | 274276.i | 1.12448 | + | 0.468668i | ||||
\(766\) | −439769. | −0.749492 | ||||||||
\(767\) | 7770.98i | 0.0132095i | ||||||||
\(768\) | 582658. | + | 116562.i | 0.987851 | + | 0.197622i | ||||
\(769\) | 321414. | 0.543515 | 0.271758 | − | 0.962366i | \(-0.412395\pi\) | ||||
0.271758 | + | 0.962366i | \(0.412395\pi\) | |||||||
\(770\) | − | 557589.i | − | 0.940443i | ||||||
\(771\) | −86751.2 | + | 433643.i | −0.145938 | + | 0.729497i | ||||
\(772\) | 892031. | 1.49674 | ||||||||
\(773\) | 618982.i | 1.03590i | 0.855410 | + | 0.517951i | \(0.173305\pi\) | ||||
−0.855410 | + | 0.517951i | \(0.826695\pi\) | |||||||
\(774\) | 208403. | − | 500025.i | 0.347874 | − | 0.834661i | ||||
\(775\) | −7304.33 | −0.0121612 | ||||||||
\(776\) | 988219.i | 1.64108i | ||||||||
\(777\) | 480009. | + | 96027.0i | 0.795074 | + | 0.159056i | ||||
\(778\) | 528026. | 0.872361 | ||||||||
\(779\) | 131531.i | 0.216747i | ||||||||
\(780\) | 20992.6 | − | 104935.i | 0.0345045 | − | 0.172478i | ||||
\(781\) | 632315. | 1.03665 | ||||||||
\(782\) | 145877.i | 0.238546i | ||||||||
\(783\) | 72602.8 | − | 107888.i | 0.118421 | − | 0.175974i | ||||
\(784\) | −52.9808 | −8.61959e−5 | ||||||||
\(785\) | 1.04249e6i | 1.69173i | ||||||||
\(786\) | −1.11740e6 | − | 223539.i | −1.80869 | − | 0.361832i | ||||
\(787\) | 402088. | 0.649190 | 0.324595 | − | 0.945853i | \(-0.394772\pi\) | ||||
0.324595 | + | 0.945853i | \(0.394772\pi\) | |||||||
\(788\) | 539807.i | 0.869333i | ||||||||
\(789\) | 181107. | − | 905299.i | 0.290925 | − | 1.45425i | ||||
\(790\) | −447825. | −0.717553 | ||||||||
\(791\) | − | 516037.i | − | 0.824760i | ||||||
\(792\) | −318539. | − | 132762.i | −0.507823 | − | 0.211653i | ||||
\(793\) | −70051.1 | −0.111396 | ||||||||
\(794\) | 130369.i | 0.206792i | ||||||||
\(795\) | 96586.5 | + | 19322.3i | 0.152821 | + | 0.0305721i | ||||
\(796\) | 1.74075e6 | 2.74733 | ||||||||
\(797\) | 99124.1i | 0.156050i | 0.996951 | + | 0.0780248i | \(0.0248613\pi\) | ||||
−0.996951 | + | 0.0780248i | \(0.975139\pi\) | |||||||
\(798\) | 171211. | − | 855831.i | 0.268860 | − | 1.34395i | ||||
\(799\) | −188880. | −0.295865 | ||||||||
\(800\) | − | 92459.8i | − | 0.144468i | ||||||
\(801\) | −185946. | + | 446145.i | −0.289816 | + | 0.695362i | ||||
\(802\) | −1.21765e6 | −1.89310 | ||||||||
\(803\) | 424048.i | 0.657634i | ||||||||
\(804\) | 1.83569e6 | + | 367234.i | 2.83980 | + | 0.568108i | ||||
\(805\) | −88913.9 | −0.137207 | ||||||||
\(806\) | 8947.94i | 0.0137738i | ||||||||
\(807\) | 35279.0 | − | 176349.i | 0.0541713 | − | 0.270786i | ||||
\(808\) | −673022. | −1.03088 | ||||||||
\(809\) | 63839.2i | 0.0975418i | 0.998810 | + | 0.0487709i | \(0.0155304\pi\) | ||||
−0.998810 | + | 0.0487709i | \(0.984470\pi\) | |||||||
\(810\) | 800027. | + | 807074.i | 1.21937 | + | 1.23011i | ||||
\(811\) | −10598.6 | −0.0161141 | −0.00805707 | − | 0.999968i | \(-0.502565\pi\) | ||||
−0.00805707 | + | 0.999968i | \(0.502565\pi\) | |||||||
\(812\) | 224440.i | 0.340398i | ||||||||
\(813\) | −8176.93 | − | 1635.81i | −0.0123711 | − | 0.00247487i | ||||
\(814\) | 481204. | 0.726240 | ||||||||
\(815\) | − | 778250.i | − | 1.17167i | ||||||
\(816\) | −683.410 | + | 3416.16i | −0.00102636 | + | 0.00513048i | ||||
\(817\) | 318738. | 0.477518 | ||||||||
\(818\) | − | 123596.i | − | 0.184713i | ||||||
\(819\) | 62228.2 | + | 25935.7i | 0.0927725 | + | 0.0386662i | ||||
\(820\) | 295574. | 0.439581 | ||||||||
\(821\) | − | 1.05519e6i | − | 1.56546i | −0.622360 | − | 0.782731i | \(-0.713826\pi\) | ||
0.622360 | − | 0.782731i | \(-0.286174\pi\) | |||||||
\(822\) | −583117. | − | 116654.i | −0.863003 | − | 0.172646i | ||||
\(823\) | −380641. | −0.561974 | −0.280987 | − | 0.959712i | \(-0.590662\pi\) | ||||
−0.280987 | + | 0.959712i | \(0.590662\pi\) | |||||||
\(824\) | 145260.i | 0.213940i | ||||||||
\(825\) | −10612.2 | + | 53047.1i | −0.0155918 | + | 0.0779388i | ||||
\(826\) | 142423. | 0.208747 | ||||||||
\(827\) | − | 365073.i | − | 0.533787i | −0.963726 | − | 0.266894i | \(-0.914003\pi\) | ||
0.963726 | − | 0.266894i | \(-0.0859973\pi\) | |||||||
\(828\) | −55311.5 | + | 132710.i | −0.0806779 | + | 0.193572i | ||||
\(829\) | 864659. | 1.25816 | 0.629080 | − | 0.777341i | \(-0.283432\pi\) | ||||
0.629080 | + | 0.777341i | \(0.283432\pi\) | |||||||
\(830\) | − | 652907.i | − | 0.947753i | ||||||
\(831\) | 1.12928e6 | + | 225916.i | 1.63531 | + | 0.327148i | ||||
\(832\) | −113588. | −0.164091 | ||||||||
\(833\) | 14816.9i | 0.0213534i | ||||||||
\(834\) | 236470. | − | 1.18204e6i | 0.339972 | − | 1.69942i | ||||
\(835\) | −805072. | −1.15468 | ||||||||
\(836\) | − | 530506.i | − | 0.759062i | ||||||
\(837\) | −48744.3 | − | 32802.3i | −0.0695781 | − | 0.0468223i | ||||
\(838\) | 984403. | 1.40180 | ||||||||
\(839\) | 802316.i | 1.13978i | 0.821720 | + | 0.569891i | \(0.193015\pi\) | ||||
−0.821720 | + | 0.569891i | \(0.806985\pi\) | |||||||
\(840\) | −736107. | − | 147260.i | −1.04324 | − | 0.208702i | ||||
\(841\) | 675460. | 0.955009 | ||||||||
\(842\) | − | 1.08076e6i | − | 1.52442i | ||||||
\(843\) | 137219. | − | 685914.i | 0.193089 | − | 0.965194i | ||||
\(844\) | −1.64939e6 | −2.31547 | ||||||||
\(845\) | − | 756177.i | − | 1.05903i | ||||||
\(846\) | −277896. | − | 115823.i | −0.388277 | − | 0.161828i | ||||
\(847\) | −497139. | −0.692964 | ||||||||
\(848\) | 481.327i | 0.000669342i | ||||||||
\(849\) | −125655. | − | 25137.6i | −0.174327 | − | 0.0348746i | ||||
\(850\) | 193071. | 0.267227 | ||||||||
\(851\) | − | 76733.4i | − | 0.105956i | ||||||
\(852\) | 436305. | − | 2.18095e6i | 0.601050 | − | 3.00446i | ||||
\(853\) | 264679. | 0.363765 | 0.181882 | − | 0.983320i | \(-0.441781\pi\) | ||||
0.181882 | + | 0.983320i | \(0.441781\pi\) | |||||||
\(854\) | 1.28387e6i | 1.76037i | ||||||||
\(855\) | −257232. | + | 617182.i | −0.351879 | + | 0.844269i | ||||
\(856\) | 1.35595e6 | 1.85053 | ||||||||
\(857\) | − | 604516.i | − | 0.823088i | −0.911390 | − | 0.411544i | \(-0.864990\pi\) | ||
0.911390 | − | 0.411544i | \(-0.135010\pi\) | |||||||
\(858\) | 64983.7 | + | 13000.1i | 0.0882734 | + | 0.0176593i | ||||
\(859\) | −444881. | −0.602917 | −0.301459 | − | 0.953479i | \(-0.597474\pi\) | ||||
−0.301459 | + | 0.953479i | \(0.597474\pi\) | |||||||
\(860\) | − | 716262.i | − | 0.968445i | ||||||
\(861\) | −36527.0 | + | 182587.i | −0.0492728 | + | 0.246300i | ||||
\(862\) | −8731.36 | −0.0117508 | ||||||||
\(863\) | − | 92519.9i | − | 0.124226i | −0.998069 | − | 0.0621132i | \(-0.980216\pi\) | ||
0.998069 | − | 0.0621132i | \(-0.0197840\pi\) | |||||||
\(864\) | 415218. | − | 617016.i | 0.556223 | − | 0.826549i | ||||
\(865\) | 845123. | 1.12950 | ||||||||
\(866\) | − | 1.89968e6i | − | 2.53305i | ||||||
\(867\) | 218295. | + | 43670.5i | 0.290406 | + | 0.0580965i | ||||
\(868\) | 101403. | 0.134589 | ||||||||
\(869\) | − | 171480.i | − | 0.227077i | ||||||
\(870\) | 54548.6 | − | 272672.i | 0.0720685 | − | 0.360248i | ||||
\(871\) | −137600. | −0.181377 | ||||||||
\(872\) | 336504.i | 0.442545i | ||||||||
\(873\) | 1.15018e6 | + | 479379.i | 1.50917 | + | 0.629000i | ||||
\(874\) | −136812. | −0.179102 | ||||||||
\(875\) | − | 693858.i | − | 0.906264i | ||||||
\(876\) | 1.46261e6 | + | 292598.i | 1.90599 | + | 0.381297i | ||||
\(877\) | −1.19525e6 | −1.55403 | −0.777014 | − | 0.629483i | \(-0.783267\pi\) | ||||
−0.777014 | + | 0.629483i | \(0.783267\pi\) | |||||||
\(878\) | 1.67512e6i | 2.17299i | ||||||||
\(879\) | 167191. | − | 835735.i | 0.216388 | − | 1.08166i | ||||
\(880\) | −2087.38 | −0.00269548 | ||||||||
\(881\) | 1.52256e6i | 1.96166i | 0.194870 | + | 0.980829i | \(0.437571\pi\) | ||||
−0.194870 | + | 0.980829i | \(0.562429\pi\) | |||||||
\(882\) | −9085.82 | + | 21799.8i | −0.0116796 | + | 0.0280230i | ||||
\(883\) | 1.38373e6 | 1.77471 | 0.887357 | − | 0.461083i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461083i | \(0.152539\pi\) | |||||||
\(884\) | − | 146246.i | − | 0.187145i | ||||||
\(885\) | −106990. | − | 21403.6i | −0.136602 | − | 0.0273276i | ||||
\(886\) | −579486. | −0.738203 | ||||||||
\(887\) | − | 952113.i | − | 1.21016i | −0.796166 | − | 0.605078i | \(-0.793142\pi\) | ||
0.796166 | − | 0.605078i | \(-0.206858\pi\) | |||||||
\(888\) | 127087. | − | 635266.i | 0.161166 | − | 0.805620i | ||||
\(889\) | 1.16762e6 | 1.47740 | ||||||||
\(890\) | 1.03355e6i | 1.30483i | ||||||||
\(891\) | −309043. | + | 306344.i | −0.389281 | + | 0.385882i | ||||
\(892\) | −1.56596e6 | −1.96812 | ||||||||
\(893\) | − | 177143.i | − | 0.222137i | ||||||
\(894\) | −1.76353e6 | − | 352798.i | −2.20652 | − | 0.441419i | ||||
\(895\) | 188001. | 0.234701 | ||||||||
\(896\) | 1.28950e6i | 1.60622i | ||||||||
\(897\) | 2073.02 | − | 10362.4i | 0.00257643 | − | 0.0128788i | ||||
\(898\) | −93006.9 | −0.115335 | ||||||||
\(899\) | 14376.9i | 0.0177887i | ||||||||
\(900\) | 175645. | + | 73206.2i | 0.216846 | + | 0.0903780i | ||||
\(901\) | 134610. | 0.165817 | ||||||||
\(902\) | 183041.i | 0.224976i | ||||||||
\(903\) | 442461. | + | 88515.4i | 0.542625 | + | 0.108553i | ||||
\(904\) | −682946. | −0.835699 | ||||||||
\(905\) | 1.36303e6i | 1.66421i | ||||||||
\(906\) | −239710. | + | 1.19824e6i | −0.292032 | + | 1.45978i | ||||
\(907\) | 727198. | 0.883972 | 0.441986 | − | 0.897022i | \(-0.354274\pi\) | ||||
0.441986 | + | 0.897022i | \(0.354274\pi\) | |||||||
\(908\) | 1.18005e6i | 1.43129i | ||||||||
\(909\) | −326479. | + | 783327.i | −0.395119 | + | 0.948016i | ||||
\(910\) | 144160. | 0.174085 | ||||||||
\(911\) | − | 748391.i | − | 0.901762i | −0.892584 | − | 0.450881i | \(-0.851110\pi\) | ||
0.892584 | − | 0.450881i | \(-0.148890\pi\) | |||||||
\(912\) | −3203.87 | − | 640.942i | −0.00385199 | − | 0.000770600i | ||||
\(913\) | 250009. | 0.299927 | ||||||||
\(914\) | 1.45012e6i | 1.73585i | ||||||||
\(915\) | 192942. | − | 964458.i | 0.230454 | − | 1.15197i | ||||
\(916\) | −493915. | −0.588655 | ||||||||
\(917\) | − | 949192.i | − | 1.12880i | ||||||
\(918\) | 1.28843e6 | + | 867045.i | 1.52889 | + | 1.02886i | ||||
\(919\) | 908418. | 1.07561 | 0.537805 | − | 0.843069i | \(-0.319254\pi\) | ||||
0.537805 | + | 0.843069i | \(0.319254\pi\) | |||||||
\(920\) | 117673.i | 0.139027i | ||||||||
\(921\) | −1.04749e6 | − | 209554.i | −1.23490 | − | 0.247045i | ||||
\(922\) | −1.90018e6 | −2.23528 | ||||||||
\(923\) | 163480.i | 0.191894i | ||||||||
\(924\) | 147325. | − | 736431.i | 0.172557 | − | 0.862557i | ||||
\(925\) | −101559. | −0.118695 | ||||||||
\(926\) | 1.27882e6i | 1.49138i | ||||||||
\(927\) | 169067. | + | 70464.6i | 0.196743 | + | 0.0819996i | ||||
\(928\) | −181985. | −0.211320 | ||||||||
\(929\) | − | 301938.i | − | 0.349853i | −0.984581 | − | 0.174927i | \(-0.944031\pi\) | ||
0.984581 | − | 0.174927i | \(-0.0559688\pi\) | |||||||
\(930\) | −123194. | − | 24645.3i | −0.142438 | − | 0.0284950i | ||||
\(931\) | −13896.1 | −0.0160322 | ||||||||
\(932\) | 2.19553e6i | 2.52760i | ||||||||
\(933\) | −19822.1 | + | 99084.6i | −0.0227712 | + | 0.113826i | ||||
\(934\) | −2.38831e6 | −2.73777 | ||||||||
\(935\) | 583766.i | 0.667753i | ||||||||
\(936\) | 34324.6 | − | 82355.6i | 0.0391790 | − | 0.0940029i | ||||
\(937\) | −788069. | −0.897604 | −0.448802 | − | 0.893631i | \(-0.648149\pi\) | ||||
−0.448802 | + | 0.893631i | \(0.648149\pi\) | |||||||
\(938\) | 2.52187e6i | 2.86627i | ||||||||
\(939\) | −380281. | − | 76076.2i | −0.431294 | − | 0.0862815i | ||||
\(940\) | −398072. | −0.450512 | ||||||||
\(941\) | 347979.i | 0.392983i | 0.980506 | + | 0.196491i | \(0.0629548\pi\) | ||||
−0.980506 | + | 0.196491i | \(0.937045\pi\) | |||||||
\(942\) | −445460. | + | 2.22672e6i | −0.502004 | + | 2.50936i | ||||
\(943\) | 29188.0 | 0.0328232 | ||||||||
\(944\) | − | 533.172i | − | 0.000598306i | ||||||
\(945\) | −528476. | + | 785317.i | −0.591782 | + | 0.879390i | ||||
\(946\) | 443562. | 0.495647 | ||||||||
\(947\) | − | 704206.i | − | 0.785236i | −0.919702 | − | 0.392618i | \(-0.871570\pi\) | ||
0.919702 | − | 0.392618i | \(-0.128430\pi\) | |||||||
\(948\) | −591460. | − | 118323.i | −0.658126 | − | 0.131660i | ||||
\(949\) | −109634. | −0.121734 | ||||||||
\(950\) | 181074.i | 0.200635i | ||||||||
\(951\) | −60683.4 | + | 303338.i | −0.0670979 | + | 0.335402i | ||||
\(952\) | −1.02589e6 | −1.13195 | ||||||||
\(953\) | 885025.i | 0.974473i | 0.873270 | + | 0.487236i | \(0.161995\pi\) | ||||
−0.873270 | + | 0.487236i | \(0.838005\pi\) | |||||||
\(954\) | 198049. | + | 82543.9i | 0.217609 | + | 0.0906960i | ||||
\(955\) | −977842. | −1.07217 | ||||||||
\(956\) | 2.64763e6i | 2.89696i | ||||||||
\(957\) | 104411. | + | 20887.6i | 0.114004 | + | 0.0228068i | ||||
\(958\) | −2.13489e6 | −2.32619 | ||||||||
\(959\) | − | 495338.i | − | 0.538597i | ||||||
\(960\) | 312855. | − | 1.56387e6i | 0.339469 | − | 1.69690i | ||||
\(961\) | −917025. | −0.992967 | ||||||||
\(962\) | 124411.i | 0.134434i | ||||||||
\(963\) | 657762. | − | 1.57818e6i | 0.709277 | − | 1.70178i | ||||
\(964\) | −221816. | −0.238693 | ||||||||
\(965\) | − | 920589.i | − | 0.988579i | ||||||
\(966\) | −189917. | − | 37993.4i | −0.203522 | − | 0.0407149i | ||||
\(967\) | 565109. | 0.604337 | 0.302169 | − | 0.953254i | \(-0.402289\pi\) | ||||
0.302169 | + | 0.953254i | \(0.402289\pi\) | |||||||
\(968\) | 657936.i | 0.702155i | ||||||||
\(969\) | −179249. | + | 896010.i | −0.190901 | + | 0.954257i | ||||
\(970\) | 2.66456e6 | 2.83192 | ||||||||
\(971\) | 1.67113e6i | 1.77244i | 0.463268 | + | 0.886218i | \(0.346677\pi\) | ||||
−0.463268 | + | 0.886218i | \(0.653323\pi\) | |||||||
\(972\) | 843385. | + | 1.27732e6i | 0.892675 | + | 1.35197i | ||||
\(973\) | 1.00410e6 | 1.06060 | ||||||||
\(974\) | 569024.i | 0.599809i | ||||||||
\(975\) | −13714.9 | − | 2743.69i | −0.0144272 | − | 0.00288620i | ||||
\(976\) | 4806.25 | 0.00504553 | ||||||||
\(977\) | 57680.8i | 0.0604285i | 0.999543 | + | 0.0302143i | \(0.00961896\pi\) | ||||
−0.999543 | + | 0.0302143i | \(0.990381\pi\) | |||||||
\(978\) | 332551. | − | 1.66232e6i | 0.347680 | − | 1.73795i | ||||
\(979\) | −395766. | −0.412927 | ||||||||
\(980\) | 31227.1i | 0.0325147i | ||||||||
\(981\) | 391655. | + | 163236.i | 0.406973 | + | 0.169620i | ||||
\(982\) | −119812. | −0.124244 | ||||||||
\(983\) | − | 704181.i | − | 0.728748i | −0.931253 | − | 0.364374i | \(-0.881283\pi\) | ||
0.931253 | − | 0.364374i | \(-0.118717\pi\) | |||||||
\(984\) | 241644. | + | 48341.5i | 0.249566 | + | 0.0499263i | ||||
\(985\) | 557089. | 0.574186 | ||||||||
\(986\) | − | 380016.i | − | 0.390884i | ||||||
\(987\) | 49193.6 | − | 245904.i | 0.0504981 | − | 0.252424i | ||||
\(988\) | 137158. | 0.140510 | ||||||||
\(989\) | − | 70731.0i | − | 0.0723131i | ||||||
\(990\) | −357969. | + | 858883.i | −0.365238 | + | 0.876322i | ||||
\(991\) | 880717. | 0.896786 | 0.448393 | − | 0.893836i | \(-0.351996\pi\) | ||||
0.448393 | + | 0.893836i | \(0.351996\pi\) | |||||||
\(992\) | 82221.9i | 0.0835534i | ||||||||
\(993\) | 669701. | + | 133975.i | 0.679176 | + | 0.135871i | ||||
\(994\) | 2.99619e6 | 3.03247 | ||||||||
\(995\) | − | 1.79648e6i | − | 1.81459i | ||||||
\(996\) | 172509. | − | 862321.i | 0.173898 | − | 0.869261i | ||||
\(997\) | 275274. | 0.276933 | 0.138466 | − | 0.990367i | \(-0.455783\pi\) | ||||
0.138466 | + | 0.990367i | \(0.455783\pi\) | |||||||
\(998\) | − | 1.11231e6i | − | 1.11677i | ||||||
\(999\) | −677735. | − | 456079.i | −0.679092 | − | 0.456993i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.5.b.a.119.9 | ✓ | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.70 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.9 | ✓ | 78 | 1.1 | even | 1 | trivial | |
177.5.b.a.119.70 | yes | 78 | 3.2 | odd | 2 | inner |